As shown in the figure, there is a solid figure with base formed by the curve $y = \sqrt{(1-2x)\cos x}$ ($\frac{3}{4}\pi \leq x \leq \frac{5}{4}\pi$) and the $x$-axis and the two lines $x = \frac{3}{4}\pi$ and $x = \frac{5}{4}\pi$. When this solid figure is cut by a plane perpendicular to the $x$-axis, all cross-sections are squares. Find the volume of this solid figure. [3 points] (1) $\sqrt{2}\pi - \sqrt{2}$ (2) $\sqrt{2}\pi - 1$ (3) $2\sqrt{2}\pi - \sqrt{2}$ (4) $2\sqrt{2}\pi - 1$ (5) $2\sqrt{2}\pi$
As shown in the figure, there is a solid figure with base formed by the curve $y = \sqrt{(1-2x)\cos x}$ ($\frac{3}{4}\pi \leq x \leq \frac{5}{4}\pi$) and the $x$-axis and the two lines $x = \frac{3}{4}\pi$ and $x = \frac{5}{4}\pi$. When this solid figure is cut by a plane perpendicular to the $x$-axis, all cross-sections are squares. Find the volume of this solid figure. [3 points]\\
(1) $\sqrt{2}\pi - \sqrt{2}$\\
(2) $\sqrt{2}\pi - 1$\\
(3) $2\sqrt{2}\pi - \sqrt{2}$\\
(4) $2\sqrt{2}\pi - 1$\\
(5) $2\sqrt{2}\pi$